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A common way to accomplish that is to find the cumulative distribution function F(x) for the distribution and then solve for x according to

F(x) = Y

x = F'(Y)

Then x will be distributed with the original distribution function, if F'(Y) is fed with random values Y ranging from 0-1.

I'm currently trying to do that with a weibull distribution

f(x) = a*b*x

^{b-1}*e

^{-a*b*x^b}

where F(x) should be

F(x) = e

^{-a}- e

^{-a*x^b}

when solving for x in F(x) I however get

x = ( - ln(e

^{-a}- Y)/a)

^{1/b}

When Y> e

^{-a}there are no real solutions. Is there a way to get around this? Have I done something wrong?